Rybakina was unable to defend her Italian Open title because of sickness and after losing serve in the opening game at Roland Garros on Tuesday to go 2-0 down, it looked like the former Wimbledon champ might be in for a troublesome morning.
She also had the memory of having to withdraw from the French Open last year before her third-round match.
"Last year I missed this tournament and it was really hard but really happy to be back and compete here," Rybakina told the Court Suzanne Lenglen crowd.
"I'm really happy, thank you so much for coming guys, it's been an amazing atmosphere."
After Minnen's fast start, fourth seed Rybakina settled down to take the next six games and win the first set, and the Kazakh began the second in the same fashion as she cruised into a 4-0 lead.
Minnen rallied and broke serve, and when Rybakina broke for a third time in the second set and served for the match, the Belgian broke again.Â
But it only delayed the inevitable as the Kazakh held her next service game to win the match.
The new roof was in use again on Lenglen, as the rain fell on Roland Garros, but Rybakina was untroubled by the conditions.
"Of course, the ball is a little bit heavier and you need to move better and it's different, but that's tennis and you need to adjust with this rainy weather," she said.
Rybakina is the only player to beat Iga Swiatek on clay this year, defeating the world No.1 and three-time French Open winner on her way to the Stuttgart title in April.
The 24-year-old will now have a couple of days rest before facing either Arantxa Rus of the Netherlands or Germany's Angelique Kerber.
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